Question: A professor has 21 students in her class. Each student will receive a grade of A, B, C, D, or F. (a) In how

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A professor has 21 students in her class. Each student will receive a grade of A, B, C, D, or F. (a) In how many ways might the professor assign a grade of A, B, C, D, or F to each of the 21 students in her class? (b) The professor's university is compiling statistics on grade distributions and requests the grade distribution (i.e., the number of students in each grade category) from this class. How many grade distributions are possible for a class of 21 students? (c) -How many grade distributions are possible for a class of 21 students if the sets of A-students, B-students, C-students, D-students, and F-students form a partition of the class?

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